* Britain's allies in the European Community began privately making known their concern at the strains developing between London and the new government in Dublin over approaches to the Ulster problem.

* The International Red Cross was able to insist that it should carry out an inspection of the Maze Prison and attempt to mediate between the hunger-striking prisoners and the British authorities.

Each of these developments found Britain less than happy about its failure to keep the Ulster crisis a domestic matter.

The Irish prime minister, Garret FirzGerald, has political as well as humanitarian motives for wanting an H-blocks settlement.

Two Maze prisoners are believed close to death, one of them Kieran Doherty, is the newly elected representative for the border area of Cavan-Monaghan in the Irish parliament. Dr. FitzGerald could lose his waferthin majority of two votes if Mr. Doherty, now on the 57th day of his fast and "deteriorating rapidly," should die.

The possibility of intervention by President Reagan worried Mrs. Thatcher especially. She asked Lord Carrington, her foreign secretary, now on a visit to the United States, to explain Britain's position on Ulster to the US secretary of state, Alexander M. Haig Jr.

But the feeling in Belfast is that President Reagan, while expressing sympathy with the suffering in Northern Ireland, will reiterate the view that the Ulster issue is an internal matter of the British government.

European worries about the hunger strike are based on assessments of the damage likely to be done to relations between London and Dublin if more prisoners die and the hunger strike issue remains unresolved.

Ireland and Britain are partners in the European Community, and officials in Brussels and other capitals fear that their relations will worsen if no solution is found.

The International Red Cross visit to the Maze is an even sharper indication that Britain is having to respond to international pressure.

Red Cross officials in Geneva have tried many times to get British permission to visit the prison but have been consistently rebuffed. Now, London has suddenly agreed.

The humanitarian purpose of the Red Cross visit was being stressed both by the Swiss and the British. An International Red Cross spokesman said, "The only role is to try to bring about a humanitarian solution, not a political solution." And Humphrey Atkins, secretary of state for Northern Ireland, emphasized: "We are not negotiating with anybody. We have a clear duty to protect the public and to carry out the sentences of the courts. But we are anxious because we are humanitarian that the conditions under which we hold people should be the best we can provide."

Behind the public statements, however, is the anxiety to find a settlement after the failure last week of the Irish Roman Catholic Commission for Justice and Peace to achieve a breakthrough. Some observers, and particularly government sources in Dublin, feel that a settlement had been prevented by British intransigence. The British claimed that the commission had been too optimistic. In the aftermath of the failure, and with the danger of further disillusionment setting in while hunger strikers near death, the latest move to involve the Red Corss is seen as an attempt to prevent total deadlock.

One key factor has been an apparent shift of policy by the Provisional wing of the illegal Irish Republican Army (IRA), which until recently has been demanding political (noncriminal) status. They have five specific demands, including reforms involving prison clothing, work conditions, and meetings together. The British seemed willing to consider some changes in these areas provided that the hunger strikes ceased. But the British held out firmly against political status.

Recently, however, the Provisionals seemed to suggest that they would accept changes that were applied equally to all inmates of Ulster prisons, thus effectively nullifying any claim to special political status. This development clearly prompted the British to invite the International Red Cross.

Obviously the British feel that the findings will be in their favor. This view was indicated tacitly by Mr. Atkins, who said: "We think conditions in the Maze stand in comparison with anywhere in the world. We are convinced of that, but let them come and look."

The Red Cross has no power to impose changes, but it can make recommendations , and in special circumstances its comments can be made public. significantly, the government wil seek the agreement of the Red Cross to publish the findings, and this is seen as an indication of Whitehall's confidence.

Meanwhile, the Provisionals have reacted cautiously, but their first comments were not encouraging. Gerry Adams, vice-president of the Provisional Sinn Fein, referred to the prisoners' five demands and said, "Obviously if the Red Cross puts pressure on the British government to concede these just demands, Sinn Fein would welcome their intervention. Otherwise we see no useful purpose being served by their visit."

Part of Britain's problem is that its own room for maneuvering is limited by the insistence of Ulster's Protestant majority that the government in London should not accord the H-block prisoners political status or anything approximating it.

On the other hand, preoccupied as they are with civil disorders in mainland Britain, the authorities are less able to withstand external presures of the kind now being exerted.

At the same time, Britons are learning that the Ulster crisis has the potential to enter their own lives.

Street disorders in over 30 cities have forced British police to consider new methods of crown control. Their attention has naturally turned to Ulster, where water cannon, plastic bullets, and armored cars are used routinely to deal with violence.

This week Mrs. Thatcher and the home secretary, William Whitelaw, announced to Parliament that the same tools would be available to police in the future for their attempts to contain riots.

The basic lesson of all this is that Ulster is no longer a self-contained problem, but a crisis impinging more and more on Britain's internal politics and external relations.

The Thatcher government is having to fight a rearguard action on the international front to make its Ulster policies better understood and to retain the political initiative in what, after all, is a British province.